Square gyrobicupolic ring (EntityTopic, 17)
From Hi.gher. Space
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The '''square gyrobicupolic ring''' is a [[CRF polychoron]] discovered by [[Keiji]]. It is a member of the family of [[bicupolic ring]]s, which contains eight other similar polychora. It is formed by attaching two [[square cupola]]e by their [[octagon]]al faces, folding them into the fourth dimension with their [[square]] ends connected by a [[square antiprism]], and then filling in the gaps with 8 [[square pyramid]]s. For faces, it contains one octagon, 10 squares and 24 [[triangle]]s. | The '''square gyrobicupolic ring''' is a [[CRF polychoron]] discovered by [[Keiji]]. It is a member of the family of [[bicupolic ring]]s, which contains eight other similar polychora. It is formed by attaching two [[square cupola]]e by their [[octagon]]al faces, folding them into the fourth dimension with their [[square]] ends connected by a [[square antiprism]], and then filling in the gaps with 8 [[square pyramid]]s. For faces, it contains one octagon, 10 squares and 24 [[triangle]]s. | ||
| + | |||
| + | == Cartesian coordinates == | ||
| + | The coordinates of the square gyrobicupolic ring are as follows: | ||
| + | <blockquote> | ||
| + | (±(1+√2),±1,0,0);<br /> | ||
| + | (±1,±(1+√2),0,0);<br /> | ||
| + | (±1,±1,√(2-{{Over|√2|2}}),√({{Over|√2|2}}));<br /> | ||
| + | (±√2,0,√(2-{{Over|√2|2}}),-√({{Over|√2|2}}));<br /> | ||
| + | (0,±√2,√(2-{{Over|√2|2}}),-√({{Over|√2|2}})). | ||
| + | </blockquote> | ||
== Equations == | == Equations == | ||
Revision as of 21:01, 22 November 2011
The square gyrobicupolic ring is a CRF polychoron discovered by Keiji. It is a member of the family of bicupolic rings, which contains eight other similar polychora. It is formed by attaching two square cupolae by their octagonal faces, folding them into the fourth dimension with their square ends connected by a square antiprism, and then filling in the gaps with 8 square pyramids. For faces, it contains one octagon, 10 squares and 24 triangles.
Cartesian coordinates
The coordinates of the square gyrobicupolic ring are as follows:
(±(1+√2),±1,0,0);
(±1,±(1+√2),0,0);
(±1,±1,√(2-√2∕2),√(√2∕2));
(±√2,0,√(2-√2∕2),-√(√2∕2));
(0,±√2,√(2-√2∕2),-√(√2∕2)).
Equations
- Variables:
l ⇒ edge length
- The hypervolumes of a square gyrobicupolic ring are given by:
total edge length = 40l
total surface area = 2(6 + √2 + 3√3) · l2
surcell volume = Unknown
bulk = Unknown
- The realmic cross-sections (n) of a square gyrobicupolic ring are:
[!x,!y] ⇒ Unknown
[!z] ⇒ Unknown
[!w] ⇒ Unknown
| Notable Tetrashapes | |
| Regular: | pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron |
| Powertopes: | triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate |
| Circular: | glome • cubinder • duocylinder • spherinder • sphone • cylindrone • dicone • coninder |
| Torii: | tiger • torisphere • spheritorus • torinder • ditorus |
